Clustering with shallow trees

We propose a new method for hierarchical clustering based on the optimisation of a cost function over trees of limited depth, and we derive a message--passing method that allows to solve it efficiently. The method and algorithm can be interpreted as a natural interpolation between two well-known approaches, namely single linkage and the recently presented Affinity Propagation. We analyze with this general scheme three biological/medical structured datasets (human population based on genetic information, proteins based on sequences and verbal autopsies) and show that the interpolation technique provides new insight.Comment: 11 pages, 7 figure

Faster Separators for Shallow Minor-Free Graphs via Dynamic Approximate Distance Oracles

Plotkin, Rao, and Smith (SODA'97) showed that any graph with $m$ edges and $n$ vertices that excludes $K_h$ as a depth $O(\ell\log n)$-minor has a separator of size $O(n/\ell + \ell h^2\log n)$ and that such a separator can be found in $O(mn/\ell)$ time. A time bound of $O(m + n^{2+\epsilon}/\ell)$ for any constant $\epsilon > 0$ was later given (W., FOCS'11) which is an improvement for non-sparse graphs. We give three new algorithms. The first has the same separator size and running time O(\mbox{poly}(h)\ell m^{1+\epsilon}). This is a significant improvement for small $h$ and $\ell$. If $\ell = \Omega(n^{\epsilon'})$ for an arbitrarily small chosen constant $\epsilon' > 0$, we get a time bound of O(\mbox{poly}(h)\ell n^{1+\epsilon}). The second algorithm achieves the same separator size (with a slightly larger polynomial dependency on $h$) and running time O(\mbox{poly}(h)(\sqrt\ell n^{1+\epsilon} + n^{2+\epsilon}/\ell^{3/2})) when $\ell = \Omega(n^{\epsilon'})$. Our third algorithm has running time O(\mbox{poly}(h)\sqrt\ell n^{1+\epsilon}) when $\ell = \Omega(n^{\epsilon'})$. It finds a separator of size O(n/\ell) + \tilde O(\mbox{poly}(h)\ell\sqrt n) which is no worse than previous bounds when $h$ is fixed and $\ell = \tilde O(n^{1/4})$. A main tool in obtaining our results is a novel application of a decremental approximate distance oracle of Roditty and Zwick.Comment: 16 pages. Full version of the paper that appeared at ICALP'14. Minor fixes regarding the time bounds such that these bounds hold also for non-sparse graph

Growing a Tree in the Forest: Constructing Folksonomies by Integrating Structured Metadata

Many social Web sites allow users to annotate the content with descriptive metadata, such as tags, and more recently to organize content hierarchically. These types of structured metadata provide valuable evidence for learning how a community organizes knowledge. For instance, we can aggregate many personal hierarchies into a common taxonomy, also known as a folksonomy, that will aid users in visualizing and browsing social content, and also to help them in organizing their own content. However, learning from social metadata presents several challenges, since it is sparse, shallow, ambiguous, noisy, and inconsistent. We describe an approach to folksonomy learning based on relational clustering, which exploits structured metadata contained in personal hierarchies. Our approach clusters similar hierarchies using their structure and tag statistics, then incrementally weaves them into a deeper, bushier tree. We study folksonomy learning using social metadata extracted from the photo-sharing site Flickr, and demonstrate that the proposed approach addresses the challenges. Moreover, comparing to previous work, the approach produces larger, more accurate folksonomies, and in addition, scales better.Comment: 10 pages, To appear in the Proceedings of ACM SIGKDD Conference on Knowledge Discovery and Data Mining(KDD) 201

Automated identification of river hydromorphological features using UAV high resolution aerial imagery

European legislation is driving the development of methods for river ecosystem protection in light of concerns over water quality and ecology. Key to their success is the accurate and rapid characterisation of physical features (i.e., hydromorphology) along the river. Image pattern recognition techniques have been successfully used for this purpose. The reliability of the methodology depends on both the quality of the aerial imagery and the pattern recognition technique used. Recent studies have proved the potential of Unmanned Aerial Vehicles (UAVs) to increase the quality of the imagery by capturing high resolution photography. Similarly, Artificial Neural Networks (ANN) have been shown to be a high precision tool for automated recognition of environmental patterns. This paper presents a UAV based framework for the identification of hydromorphological features from high resolution RGB aerial imagery using a novel classification technique based on ANNs. The framework is developed for a 1.4 km river reach along the river Dee in Wales, United Kingdom. For this purpose, a Falcon 8 octocopter was used to gather 2.5 cm resolution imagery. The results show that the accuracy of the framework is above 81%, performing particularly well at recognising vegetation. These results leverage the use of UAVs for environmental policy implementation and demonstrate the potential of ANNs and RGB imagery for high precision river monitoring and river management